Forced Heat Transfer Check - MapleSim Help

Forced Heat Transfer Check

Accessory component to check the heat transfer coefficient of forced convection

 Description The Forced Heat Transfer Check component models the heat transfer coefficient calculation of forced convection. Before using HeatConvection component, you can check how to calculate the heat transfer coefficient internally.

Equations

Average temperature is:

$T=\frac{\mathrm{Tin}\left[1\right]-\mathrm{Tin}\left[2\right]}{2}$

Heat transfer coefficient of forced convection is calculated with:

( $h=\frac{\mathrm{Nu}\cdot k}{X}$ )

Output is:

$\mathrm{out}=h$

And, Nusselt number $\mathrm{Nu}$ is calculated with the following equation which is selected by the option.

 • Default : Use references for Forced = false

If you select this option, the generalized equation is valid.

$\mathrm{Nu}={C}_{\mathrm{forced}}\cdot \left({\mathrm{Re}}^{{m}_{\mathrm{forced}}}-{\mathrm{offset}}_{\mathrm{forced}}\right)\cdot {\mathrm{Pr}}^{{n}_{\mathrm{forced}}}$

( $\mathrm{Re}$ and $\mathrm{Pr}$ and $k$ is calculated from $\mathrm{pin}$ and $T$ )

The default value of the experimental parameters are for the flat plate with the laminar flow.

$\mathrm{Nu}=0.664\cdot {\mathrm{Re}}^{\frac{1}{2}}\cdot {\mathrm{Pr}}^{\frac{1}{3}}$



 • Reference "Tube and Duct" : Use references for Forced = true and Forced Convection type = Tube and Duct

For laminar flow, the constant Nusselt number is used in this option, and for turbulent, Dittus-Boetter's equation [1] is used.

$\mathrm{Nu}=$${\begin{array}{cc}3.66& \mathrm{Re}<2300\\ {\begin{array}{cc}0.023\cdot {\mathrm{Re}}^{0.8}\cdot {\mathrm{Pr}}^{0.4}& T\left[1\right]

( $\mathrm{Re}$ and $\mathrm{Pr}$ and $k$ is calculated from $\mathrm{pin}$ and $T$ )

 • Reference "Over flat plates (Laminar)" : Use references for Forced = true and Forced Convection type = Over flat plates

$\mathrm{Nu}=0.664\cdot {\mathrm{Re}}^{\frac{1}{2}}\cdot {\mathrm{Pr}}^{\frac{1}{3}}$

( $\mathrm{Re}$ and $\mathrm{Pr}$ and $k$ is calculated from $\mathrm{pin}$ and $T$ )

 • Reference "Over a cylinder" : Use references for Forced = true and Forced Convection type = Over a cylinder

This equation is given by Churchill and Bernstein [2], which is valid for the range ${\mathit{10}}^{\mathit{2}}\mathit{<}\mathrm{Re}\mathit{<}{\mathit{10}}^{\mathit{7}}$, $\mathrm{Re}\cdot \mathrm{Pr}>0.2$.

$\mathrm{Nu}=0.3+\frac{0.62\cdot {\mathrm{Re}}^{\frac{1}{2}}\cdot {\mathrm{Pr}}^{\frac{1}{3}}}{{\left(1+{\left(0.4\cdot \mathrm{Pr}\right)}^{\frac{2}{3}}\right)}^{\frac{1}{4}}}\cdot {\left(1+{\left(\frac{\mathrm{Re}}{282000}\right)}^{\frac{5}{8}}\right)}^{\frac{4}{5}}$

( $\mathrm{Re}$ and $\mathrm{Pr}$ and $k$ is calculated from $\mathrm{pin}$ and $T$ )



 • Reference "Over a sphere" : Use references for Forced = true and Forced Convection type = Over a sphere

This equation is developed by Whitaker [3], which is valid for the range $3.5<\mathrm{Re}<8\cdot {10}^{4}$, $0.7<\mathrm{Pr}<380$.

$\mathrm{Nu}=2+\left(0.4\cdot {\mathrm{Re}}^{\frac{1}{2}}+0.06\cdot {\mathrm{Re}}^{\frac{2}{3}}\right)\cdot {\mathrm{Pr}}^{0.4}\cdot {\left(\frac{\mathrm{η__f}}{\mathrm{η__s}}\right)}^{\frac{1}{4}}$



( $\mathrm{Re}$ and $\mathrm{Pr}$ and $k$ is calculated from $\mathrm{pin}$ and $T$ )

For information on the calculation of Fluid properties, see Fluid Properties Check.

References

[1] : Dittus, F. W. and L. M. K. Boelter, Univ. Calif. (Berkeley) Pub. Eng. vol. 2, p.443, 1930.

[2] : Churchill, S. W., and M. Bernstein. "A Correlating Equation for Forced Convection from Gases and Liquids to a Circular Cylinder in Crossflow", J. Heat Transfer, vol.99, pp.300-306, 1977.

[3] : Whitake, S. "Forced Convection Heat-Transfer Correlations for Flow in Pipes, Past Flat Plates, Single Cylinders, Single Spheres, and Flow in Packed Bids and Tube Bundles", AIChE J., vol.18 p361, 1972.

Variables

 Symbol Units Description Modelica ID $\mathrm{T__}$ $K$ Averaged temperature between Tin[1] and Tin[2] $h$ $\frac{W}{{m}^{2}\cdot K}$ Heat transfer coefficient h $\mathrm{Nu}$  Nusselt number $\mathrm{Re}$  Reynolds number $\mathrm{Pr}$  Prandtl number $k$ $\frac{W}{m\cdot K}$ Thermal conductivity $\mathrm{η__s}$ $\mathrm{Pa}\cdot s$ Viscosity calculated with temperature of solid port $\mathrm{η__f}$ $\mathrm{Pa}\cdot s$ Viscosity calculated with temperature of fluid port

Connections

 Name Units Condition Description Modelica ID $\mathrm{pin}$ $\mathrm{Pa}$ - Pressure input pin $\mathrm{Tin}\left[2\right]$ $K$ - Temperature inputs Tin[2] $\mathrm{Vin}$ $\frac{m}{s}$ - Wind speed Vin $\mathrm{out}$ $\frac{W}{m\cdot K}$ - Heat transfer coefficient of Forced convection out

Parameters

 Symbol Default Units Description Modelica ID $\mathrm{false}$  If true, all parameters are defined by references. use_reference_forced  Geometry type of forced convection as references ForcedConvecType $X$ $1.0$ $m$ Streamwise length X ${C}_{\mathrm{forced}}$  $0.664$  Gain parameter for Reynolds number in the generalized experimental equation of Forced convection generalized equation. C_forced ${m}_{\mathrm{forced}}$ $\frac{1}{2}$  Exponent parameter for Reynolds number in the generalized experimental equation of Forced convection generalized equation. m_forced ${\mathrm{offset}}_{\mathrm{forced}}$ $0$  Offset parameter for Reynolds number in the generalized experimental equation of Forced convection generalized equation. offset_forced ${n}_{\mathrm{forced}}$ $\frac{1}{3}$  Exponent parameter for Prandtl number in the generalized experimental equation of Forced convection generalized equation. n_forced

Initial Conditions

 Symbol Units Description Modelica ID $K$ Initial condition of the averaged temperature T(0)